Health Secretary Robert F. Kennedy Jr. faced a tricky moment on Tuesday when he released a report outlining President Trump’s “Make America Healthy Again” strategy.

Asked by a reporter if he agreed with Mr. Trump’s comment that vaccines work, “pure and simple,” Mr. Kennedy, a famous vaccine skeptic, at first ducked the question. “I agree with that,” Mr. Kennedy finally said. Mr. Trump’s top domestic policy adviser, who presided over the event, banged his gavel, bringing questions to a close.

The awkward scene capped a particularly fraught two weeks for the president and his celebrity health secretary. While there is no evidence that Mr. Trump is going to break with Mr. Kennedy, the secretary has lately caused consternation among some of the president’s aides and the president himself for a series of negative headlines about chaos inside the Centers for Disease Control and Prevention, and about his views on vaccines.

The White House projected itself as unbothered when Mr. Kennedy pushed out Susan Monarez, the C.D.C. director, just one month after the Senate confirmed her. But two people briefed on what took place said Mr. Trump — who declared Dr. Monarez “an incredible mother and dedicated public servant” when he nominated her — was irritated by the situation and all the negative coverage.

Mr. Kennedy’s sharp criticism of Covid-19 vaccines has also been a sticking point. In recent days, White House officials — though not Mr. Trump directly — sent Mr. Kennedy and his advisers a message telling him to tone down his rhetoric, according to two people briefed on the discussions.

That is partly because of concerns the White House has heard from some allies about Mr. Kennedy’s comments, as well as Mr. Trump’s own pride in Operation Warp Speed, the initiative that produced the shots in his first term.